Another customer has since come forward to claim Mr Duffy made "inappropriate" comments to her in response to her feedback.
The customer said she emailed the burger caravan last July, after she was dissatisfied with the restaurant's food.
"I have been to Ekim a number of times now... I have since come to the conclusion that I have ordered wrongly each time as I have never left feeling completely satisfied, and in fact haven't had a good Ekim burger experience," the woman's email to Ekim Burgers read.
"More importantly, the burgers (I am vegetarian and was excited by the array of choice you provide) have never offered quite the flavour hit I expected."
In the email, she described her comments as "concerns rather than complaints".
When Mr Duffy responded, he asked the woman to send through a photo of herself, so he could tell his staff what she looked like.
"This will help us very much, making you easily spotted will make it way easier to tell you to f*** off in person.....," Mr Duffy's response read.
When the woman replied, calling his comments "overly aggressive and incredibly rude", Mr Duffy told the woman to "find a real issue to champion".
The woman said she was shocked by Mr Duffy's attitude.
"Of course eateries - like Ekim - should be proud of their food and it's hard to receive criticism, no matter how harsh. I wasn't expecting a voucher or a huge thanks, or anything in return for that matter, it was just a comment for them to be aware of.
"I totally understand his point... But that gives him absolutely no excuse to take this out on those customers who do say something with perfectly legitimate (or well-backed up) reasoning."
When asked for comment today, Mr Duffy remained unapologetic.
"If you don't like what I'm doing on a personal level, if you don't like me that's your choice. If I don't like you, that's my choice.
"If you don't like what I am doing you don't have to come here, but I'm not going to change what I am doing, just because you don't like it.
"The business has gone from nothing to very popular and successful, because we do what we do, the way we do it.
"If I was to change everything I did for every person that didn't like something about it, it would suffer total identity crisis and everyone would come out alienated because no one would like it."
Mr Duffy said the issue had been blown out of proportion and taken out of context, and his critics had been more insulting than he had ever been.
"The people who have been unimpressed have been more attacking, more abusive, and more hurtful and insulting than anything that I have said.
"What it was, was a direct attack against the individuals that don't respect people... It's about the inequality and the total lack of respect for the service industry, and the service industry in general."
Public relations and crisis communications expert Fleur Revell said eateries needed to steer clear of public interaction with customers, no matter what the situation.
"The old saying 'the customer is always right' may not be based in truth, but the idea behind it is still as relevant today as ever," she said.
"If a restaurant appears to be judging its customers, treats them with a lack of respect, or seems to be ungrateful for their custom, people will simply find other places to eat."
